SLAHQR (3lapack)

i an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decomposition already computed by SHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI

SYNOPSIS

  SUBROUTINE SLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ,
                     Z, LDZ, INFO )

      LOGICAL        WANTT, WANTZ

      INTEGER        IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N

      REAL           H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )

PURPOSE

  SLAHQR is an auxiliary routine called by SHSEQR to update the eigenvalues
  and Schur decomposition already computed by SHSEQR, by dealing with the
  Hessenberg submatrix in rows and columns ILO to IHI.

ARGUMENTS

  WANTT   (input) LOGICAL
          = .TRUE. : the full Schur form T is required;
          = .FALSE.: only eigenvalues are required.

  WANTZ   (input) LOGICAL
          = .TRUE. : the matrix of Schur vectors Z is required;
          = .FALSE.: Schur vectors are not required.

  N       (input) INTEGER
          The order of the matrix H.  N >= 0.

  ILO     (input) INTEGER
          IHI     (input) INTEGER It is assumed that H is already upper
          quasi-triangular in rows and columns IHI+1:N, and that H(ILO,ILO-1)
          = 0 (unless ILO = 1). SLAHQR works primarily with the Hessenberg
          submatrix in rows and columns ILO to IHI, but applies
          transformations to all of H if WANTT is .TRUE..  1 <= ILO <=
          max(1,IHI); IHI <= N.

  H       (input/output) REAL array, dimension (LDH,N)
          On entry, the upper Hessenberg matrix H.  On exit, if WANTT is
          .TRUE., H is upper quasi-triangular in rows and columns ILO:IHI,
          with any 2-by-2 diagonal blocks in standard form. If WANTT is
          .FALSE., the contents of H are unspecified on exit.

  LDH     (input) INTEGER
          The leading dimension of the array H. LDH >= max(1,N).

  WR      (output) REAL array, dimension (N)
          WI      (output) REAL array, dimension (N) The real and imaginary
          parts, respectively, of the computed eigenvalues ILO to IHI are
          stored in the corresponding elements of WR and WI. If two
          eigenvalues are computed as a complex conjugate pair, they are
          stored in consecutive elements of WR and WI, say the i-th and
          (i+1)th, with WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the
          eigenvalues are stored in the same order as on the diagonal of the
          Schur form returned in H, with WR(i) = H(i,i), and, if
          H(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) =
          sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i).

  ILOZ    (input) INTEGER
          IHIZ    (input) INTEGER Specify the rows of Z to which
          transformations must be applied if WANTZ is .TRUE..  1 <= ILOZ <=
          ILO; IHI <= IHIZ <= N.

  Z       (input/output) REAL array, dimension (LDZ,N)
          If WANTZ is .TRUE., on entry Z must contain the current matrix Z of
          transformations accumulated by SHSEQR, and on exit Z has been
          updated; transformations are applied only to the submatrix
          Z(ILOZ:IHIZ,ILO:IHI).  If WANTZ is .FALSE., Z is not referenced.

  LDZ     (input) INTEGER
          The leading dimension of the array Z. LDZ >= max(1,N).

  INFO    (output) INTEGER
          = 0: successful exit
          > 0: SLAHQR failed to compute all the eigenvalues ILO to IHI in a
          total of 30*(IHI-ILO+1) iterations; if INFO = i, elements i+1:ihi
          of WR and WI contain those eigenvalues which have been successfully
          computed.